$\dfrac{ 10l + 6m }{ -7 } = \dfrac{ 8l + 3n }{ -6 }$ Solve for $l$.
Answer: Multiply both sides by the left denominator. $\dfrac{ 10l + 6m }{ -{7} } = \dfrac{ 8l + 3n }{ -6 }$ $-{7} \cdot \dfrac{ 10l + 6m }{ -{7} } = -{7} \cdot \dfrac{ 8l + 3n }{ -6 }$ $10l + 6m = -{7} \cdot \dfrac { 8l + 3n }{ -6 }$ Multiply both sides by the right denominator. $10l + 6m = -7 \cdot \dfrac{ 8l + 3n }{ -{6} }$ $-{6} \cdot \left( 10l + 6m \right) = -{6} \cdot -7 \cdot \dfrac{ 8l + 3n }{ -{6} }$ $-{6} \cdot \left( 10l + 6m \right) = -7 \cdot \left( 8l + 3n \right)$ Distribute both sides $-{6} \cdot \left( 10l + 6m \right) = -{7} \cdot \left( 8l + 3n \right)$ $-{60}l - {36}m = -{56}l - {21}n$ Combine $l$ terms on the left. $-{60l} - 36m = -{56l} - 21n$ $-{4l} - 36m = -21n$ Move the $m$ term to the right. $-4l - {36m} = -21n$ $-4l = -21n + {36m}$ Isolate $l$ by dividing both sides by its coefficient. $-{4}l = -21n + 36m$ $l = \dfrac{ -21n + 36m }{ -{4} }$ Swap signs so the denominator isn't negative. $l = \dfrac{ {21}n - {36}m }{ {4} }$